Apple Pay is used in physical stores and websites that support it.
It has nothing to do with apps dowloaded from the App Store or subscriptions started from there.
That uses payment methods from your Apple Account, which is unrelated to Apple Pay.
If you started the subscription from the website directly, then that subscription is outside the Apple ecosystem and must be managed directly through the Starz website. It would not be tied to your Apple Account so will not appear on your subscription list on your Apple account.
As the subscriptions are separate, and independent one has no bearing on the other.
You need to complete the payment started on your Apple Account and then cancel the subscription on Apple's platform and request a refund if you want to continue with the external subscription.
click here ➜ If you want to cancel a subscription from Apple - Apple Support
and here ➜ Request a refund for apps or content that you bought from Apple - Apple Support